Dealing with a student who is distressed or whose behavior is causing distress to others is complex. There is not single "right" way to approach a student. You have your own style of approaching and responding to others. Furthermore, we each have differing capacities to deal with others' problems and distress. It is important to know your personal limits as a helper.
If you choose to help a distressed student, or if a student approaches you to talk about personal problems:
If you are concerned about a student's suicide potential, keep in mind that mental health professionals assess suicide potential, in part, by asking if the student has a plan for exactly how he/she would act on these thoughts, when and where the student intends to carry out the plan, and if he/she has ever attempted suicide before.
The more specific and lethal the plan, act of making a previous attempt and the accessibility to carry out the plan, the higher the risk that a suicide will occur.
You need not be afraid to ask these questions. These questions will not furnish them with new ideas. Most people who are actively suicidal are willing to answer these questions. Conversely, many people consider suicide from time to time in passing. The less specific and lethal the plan (e.g., "I guess I'd take a couple sleeping pills sometime"), the less likely a suicide attempt, although one should not dismiss references to seemingly non-lethal means of attempting suicide.